As someone who has a degree in math, I still can't help but think mathematicians are getting a little bit of a comeuppance. In a lot of areas of mathematics there had been little effort to make the work understandable and leaves numerous folks who could benefit from the knowledge on the outside looking in. Now AI comes along and do the same to mathematicians. Makes me chuckle a little bit.
This feels backwards. I frequently joke "physics is the subset of mathematics that reflects the observable world". Math can be as abstract as it wants, but physics has a constraint. It must model an observable world (related, this us part of why people say String Theory is math and not physics)
Never been my experience of maths, which is one of the most accessible disciplines to have ever existed.
I also have a degree, but mostly taught myself the important undergrad-level concepts as a kid. I just went to the library and borrowed any of the hundreds of books written to clearly communicate maths to beginners or downloaded any of the free ebooks / lecture notes.
Name a single field of endeavor that is more open in 2026. Software certainly isn't one of them - the best stuff has always been gatekept.
I think you're a little naive if you think this is because of gate-keeping by mathematicians rather than the essential complexity of mathematics. Mathematicians individually and as a group would love nothing more than a world which is capable of understanding their work more deeply.
In the exact same way that LLMs allow anyone to vibe code an app but do not replace real understanding of system design due to its essential complexity, non-mathematicians will quickly learn that asking an LLM to pump out advanced mathematical statements to you, even if they are correct (and even if you could verify them) does not constitute understanding, and that the human brain is the bottleneck either way.
It is only if the LLM is super-human at simplification and explaining that a difference will be noted. This would be excellent for mathematics but its not a foregone conclusion (and the argument of most mathematicians, such as Terence Tao, is that this distillation process is one of the key parts of doing mathematics, and that LLMs so far seem to be going in the opposite direction. I suspect its probably user error and leveraging the tools better will produce different outcomes, but mathematicians are only just starting the journey that software developers have been going through, so patience is needed).
Folks keep using the word "gate keeping" -- I never used that term nor implied intentional gate keeping. It's simply not caring if those outside the club understand -- there is no one guarding the door its just folks don't care if anyone finds it.
Gatekeeping is a human universal. Even those who preach maximum inclusion do exclude plenty, of course there is always explanation why that doesn't count. If you try to run any community you quickly learn the importance of gatekeeping. Eternal September etc. See any site or fandom that gets mainstream etc. I don't think anyone has any duty to actively pull in as many as possible new people. Zen masters used to chase away students or make them sit on their doorstep for days and send them away anyway. Now, the west is essentially Christian and so the missionary impulse is real, but it doesn't work without the other stuff in the package.
Why should we expect everyone to be both a great researcher and communicator? The obvious result is that it is as effective as engineering managers. Sure, there's some amazing ones, but most aren't. Though that also doesn't mean no expertise in the field (i.e. non-engineering manager) is any better. It is just that managing/communicating is a different and orthogonal skill.
What needs to happen is we need to make it okay for people to specialize in more things. More nuance to this rather than trying to throw everyone into nice easy to manage buckets. Those buckets are just unrealistic abstractions filled with hope, denial, and laziness. Reality is surprisingly complex. Math can do a really good job helping you understand that, but it's a sufficient condition, not a necessary one
It is not lowering the bar to find better ways to demystify and explain things. In fact, I would say those who can explain it well understand it the best. Richard Feynman would be my best example.
Do you have any examples of places you felt like there was a lot of gatekeeping? Perhaps having studied mathematics I am a bit blind to the issue here and would like to learn more.
I agree making simple things sound complicated to appear more impressive is bad but there are limits. Even with Feynman he could only go so far, e.g. his interview about why questions and magnetism.
I am not thinking of intentional gatekeeping, but more of the kind where mathematicians build themselves their own island of concepts and notation with no thought of building a passageway for others to engage and make use of the theory.
I would find modern algebraic geometry highly useful as someone who works in computer graphics and computer vision, but much of the theory is akin to learning a new language and I don't get the sense that those who publish their work in this field care if I enter their world.
I do think in a lot of fields there is a lot of impact/influence to be had by people who are willing to do work to bridge different fields. I wonder to what degree this is because practitioners don't always see how their work could be used elsewhere.
I would say that it is lowering the bar to "find better ways to demystify and explain things." But there is no harm to this bar falling, because this is a bar for entry. There is a separate bar for making research discoveries (being credited for them, specifically), and that one should not be lowered, because it is a bar of standards.
We have seen the thing in programming. I'm not a gatekeeper, I love seeing more people to code. On the other hand, along the way, we lost the joy of the journey and only fixated at the destination.
Result is more software at lower quality. The reason is statistics. When you increase the population, you increase the population of every kind of programmer, and people who want the result are favored in most competitive sectors because corporations want something somewhat working yesterday.
...and here we are.
Now programmers talking about code quality is stoned en-masse. If it's somewhat working then it's good. Efficiency, resiliency, maintainability and sustainability is an afterthought. Some of my friends who loved debating programming language theory now don't even care about the code. They don't write it, just vibe, and they don't plan to come back to "older, caveman style of development".
Some universities are also adding fuel to the fire: They "prepare students for the job", not teaching the science, but the parts that corporations need for the job only.
Though, hardware was cheap and people were expensive, and now code is cheap and hardware is expensive now. We'll see.
The point I was trying to make was not "enjoying the process for the sake of it", but paying attention and spending effort on the journey created better software at the end.
When you look at older software, most of it was higher quality than the things we have today. A web site contained more information in a more readable way, more features in a smaller footprint. Same for native applications.
Now we slap what we found online together and calling it done. Everything is sparse, takes ages to load, centuries to submit and everything is so disconnected and async that some simple features are straight out impossible.
This is what fixating on the destination brought us. I dare you to download something you purchased 3 months ago via a 4096 character S3 link they have sent you, and double dare you to ask customer support for a new link. I'll bet that with a 80% chance they have no way to verify your serial number, even.
Have people completely forgotten how to read? I'm saying your analogy between software and math is completely, irreconcilably flawed. I don't need to read the rest of your screed because this is a thread about math not software.
Somebody said that lowering the bar is not good. Somebody else asked for examples, and I provided an example. So, if you want to be pedantic, that doesn't track well, because what I answered was not about mathematics.
If you want something about mathematics, computation is mathematics, as software is. So, my example tracks the same way in mathematics.
Finding solutions without understanding its parts or the path is equally detrimental to mathematics as it is detrimental to software.
Maybe you need to read a bit slower and think along the way. Using AI too much blunts critical thinking skills in some, as I read.
What was the end of the proof thing you mathematicians use, was it "Q.E.D."?
> computation is mathematics, as software is. So, my example tracks the same way in mathematics.
brother i already addressed this literally in my first response to you: the reason software went to shit is because it became commodified (ie a thing produced in a factory) not because it's computational nor because the bar got lowered. seriously read my whole original reply again and see whether you really disagree before just re-asserting your rant on SWE.
> Finding solutions without understanding its parts or the path
you didn't read the post at all did you? it's emphatically about deep understanding over blind results.
> Using AI too much blunts critical thinking skills in some, as I read.
Half of modern academia, for one. Universities have turned into degree mills with the expectation that >50% of the population requires a college degree, regardless of whether they actually have any interest or need for one beyond doing it because it's a prerequisite for a good career, independent of whether said career actually uses the knowledge in any way.
Not that I actually agree that math was at the right level of gatekeeping. It definitely feels intentionally opaque beyond reason, and I think it's why LLMs are able to cut through the obfuscation and solve problems that maybe wouldn't actually have been considered quite so hard if mathematicians did a better job of making their work accessible.
I too have a degree in math and it's easy to see some of what's happening as too much of an emphasis on intellectual chest thumping and to little emphasis on showing why understanding the concepts is useful for everyone. I will say the problem may well increased here by the American education system which denigrates such understanding and isn't influenced by mathematicians.
But also, with things rapidly changing, perhaps in ten years chat programs will not only do superhuman but make their proofs marvelously accessible and provide incredible tutoring sufficient to bring any curious up to a super high level quickly. Then what can you say and what can you complain of.
But I think "do everything machines" are necessarily inevitable but the situation does make it uncertain where the limits are.
I would say the research university is getting comeuppance.
Pedagogy is the primary purpose of educational institutions. That includes universities. However, when research is placed first, you are often left with mediocre teachers, because "who cares?" They were hired to do research and lend the university that kind of prestige; teaching is an afterthought squeezed into the spaces that remain.
And frankly, we haven't the faintest clue today what education is even for. That doesn't bode well.
Add to this the other troubles facing the university, like declining attendance, skyrocketing costs, and AI cheating and we're in for a very interesting transition indeed.
LLM's may have provided a bit of comeuppance. Many mathematicians have cared little if anyone understands their obscure nomenclature and build mote around their work. Now they have encountered something that is becoming far more capable than they are and they may soon be left in the dark.
There has been a steady decline for decades. Release early, release often. One example: Apple used to have a thing called Gold Master release when updating software was not as immediate. The GM programs met a high bar for quality. Not so much anymore… the attitude is we can just release a new version later this week. There also used to be a thing called backwards compatibility… now no one thinks twice about breaking code on older platforms.
That is exactly what I was thinking. I was a seasoned C++ programmer and always loved reading articles like this. I can't imagine I will every write my own C++ code again -- or in any language. I now program with English specifications now and I am 10000% times more productive.
Some of us are professionals and like to understand our systems and how they work. I don't write assembly instructions by hand either, nor do I design CPUs much, but I want to - and likely need to - know how they work to make the best judgements.
I could imagine that in near future when token prices are as high as they really are, programmers that can't imagine or remember how to write code anymore will clean our streets, drive our taxis and water our plants.
The main iPhone app I maintain for work is 100% claude edited now ... I don't touch the code anymore ... I do occasionally look at it. It does a way better job than I could. I do have Xcode open as claude does its thing ... and I occasionally sign and deploy with Xcode. No coding though.
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